Question

Arun is instructed to clap every time the count of the instructor reaches a multiple of 3. Varun is instructed to clap every time the count reaches a multiple of 7. By the time when both of them clap simultaneously for the third time, how many times did Arun clap?

• A. 21
• B. 22
• C. 25
• D. 27

Answer 1

The correct option is A 21

For Arun and Varun to clap together, the count has to be a multiple of both 3 and 7.
LCM of 3 and 7 is 21.
So, they will clap together every time the count reaches a multiple of 21.
The third time they clap together, the count will be $21\times 3=63.$
We need to find the number of times Arun has clapped when the count reaches 63.
Now, every time the count reaches a multiple of 3, Arun claps. The counts at which he claps forms an AP with the first term as 3 and the common difference also being 3.
$n^{th}$ term of the AP = 3 + (n-1)3 = 3n
3n = 63, or n = 21
Hence, Arun would have clapped 21 times.